Two-monitor UI application

I'm writing an application using two screens. The main idea is that one screen shows in fullscreen and on top of every other component (eg. OSD from OS is not allowed) an image. The controls of this view should be displayed on another display.
Several problems occured till now:

How to figure out which screen is the one I need (figure out the model name would be a solution).

Set the displaying ui component in fullscreen to this particular screen.

Forbid anything to go ontop of the display.

We're working with QtQuick 2 on an linux OS.

For the first problem: I could assure the monitor for controlling is accessed via displayPort and the other one via HDMI so I would have to figure out which screen is connected to HDMI.

For the second problem: I tried to use QWindow::setScreen() but no matter which screen I choose the window is displayed on the screen marked as main.
I could configure another X11-Server for the displaying screen. Is there a way to choose which XServer should be used to display the image? (This should also work for disallowing OSD etc. problems mentioned at point 3).

For the last point I thought of setting the Qt::X11BypassWindowManagerHint flag.

Edit:
It's also an option to use QtWidget for the display and QtQuick for the controls if there's a solution for Widgets.

It didn't work. Right now I'm trying to get it via two separate xserver sessions (one on each screen) running. When trying to set a QWindow to the other screen the application output tells me:

Xlib: extension "NV-GLX" missing on display ":0".

I'm running a GTX980 with nvidia-361 drivers from the repo and let nvidia-xconfig configure the xserver.
For running separate xserver on each screen I chose to add another XServer in the nvidia-settings dialog for display configuration.
It would be ok if I start two different applications on each screens and setup an IPC or use a second video card for the second display.

It didn't work in terms of it doesn't matter which display I chose the application window always appears on the primary screen. Though I can move the application on another screen via the move method. Then if I want to set the application to fullscreen it appears in fullscreen on the primary display again.

first of all I put my screen far away from the main screen (virtual screen position offset to at least one screen size in any dimension so I don't accidentally get tooltips on top of my image).
Then I put the secondary window to this screen via moveframe and set it to the screen resolution imitating a borderless fullscreen mode.
Finally I set the SplashScreen flag so nothing gets on top of the image. Still, it's not the solution I hoped for since I have to figure out the position and the resolution of the second screen myself instead of put the window to a specific screen and tell it to be fullscreen there but it works.